The marching band that played “Don’t Stop Believin’” has gone home. The yellow 1955 Corvette that the governor drove to the ribbon-cutting is safely garaged. The dignitaries are off dignifying other things.

The first span of the soaring, $4 billion Hudson River crossing known as the Mario M. Cuomo Bridge has been open for business since early Saturday morning.

It is gleaming and sleek and airy, especially compared to its predecessor, the rickety, rackety Tappan Zee Bridge, which will remain open in the other direction until the fall.

On Tuesday, at the first highway rest stop west of the new bridge, the reviews were unanimous.

“Very impressive!” said Susan Richter, a retired teacher from Long Island waiting for her Starbucks order at the Sloatsburg Travel Plaza of the New York State Thruway. She had changed her normal route to Syracuse so she could see for herself if the bridge, with its cables draped gracefully from tall white columns, lived up to the hype.

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The opening ceremony for the bridge last week included a marching band.CreditKevin Hagen for The New York Times

“It’s much bigger, and it’s much better,” Robert Lopez, 49, of Newburgh, said as he stopped by the travel plaza’s tourism counter. “It’s wider, it’s cleaner and it feels more secure.”

It is a bit early for meaningful traffic statistics – volume at the bridge was up slightly over the weekend compared to the same time last year, though there could be many reasons for that. And the bridge will face its first real challenge over the Labor Day weekend, a time of notorious traffic jams.

State officials say there have been no accidents on the new bridge as of Wednesday evening, though it has not been immune to delays. On Monday evening, The Journal News, which covers Westchester and Rockland Counties and has been monitoring the bridge’s cameras, reported that traffic on the approach to the Cuomo bridge was backed up about five miles, all the way to White Plains.

The project manager for the new bridge, Jamey Barbas, gazed down 270 feet from the top of one of the bridge’s towers to the roadway on Wednesday morning and liked what she saw. “I was looking to see if there were any sorts of issues, and traffic was flowing nicely,” she said.

Even on the old bridge, Ms. Barbas said, “it actually looks like it’s flowing a little better.” By closing off the westbound traffic lanes, which have moved to the new bridge, “psychologically we gave the drivers a little more room.”

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After driving over the new bridge, Solomon Wasserman, at the Sloatsburg Travel Plaza, made up a song about it.CreditStephen Speranza for The New York Times

Her boss, Gov. Andrew M. Cuomo, who named the bridge for his father, said in a statement on Wednesday, “The opening of the first span of the Mario M. Cuomo Bridge has restored New Yorkers’ confidence in our government’s ability to build bigger and smarter with speed and innovation.”

The bridge is making a few of our neighbors to the north a little jealous.

“I wish they would build that in Montreal,” Karine Mortier said as she finished her lunch at the Sloatsburg rest area.

In her hometown, the Champlain Bridge, an older steel structure that looks a bit like the Tappan Zee, is being replaced by a cable-stayed bridge that looks similar to the Cuomo bridge. “And I sure wish they built the Champlain Bridge as quickly,” said Ms. Mortier, 47, an engineering manager for Nabisco.

New York’s new bridge was actually two decades in the making, if you count the years of planning and plan-scrapping. But in any case, the entire bridge is scheduled to open next year.

In the rest area’s tourist information room, Eileen Burns, a customer service agent, said that when she asks visitors if they drove over the bridge, those that have get very excited. “They all say it’s beautiful,” she said.

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J.J. Coviello, a custodian at the Sloatsburg Travel Plaza, said he was “thrilled” about an upcoming trip over the new bridge.CreditStephen Speranza for The New York Times

Some who haven’t, like David Berkowitz, are looking forward to the experience. Mr. Berkowitz, a biomedical engineer from Philadelphia, was on his way to Schenectady, N.Y., and therefore did not need to cross the Hudson River. Nevertheless, he said, he briefly considered making a detour just to drive over the new bridge. “I just wanted to see it,” he said.

J.J. Coviello, a custodian at the service plaza, plans to cross the bridge next month when he visits family on Long Island.

“I’m thrilled,” said Mr. Coviello, 26. “It’s a good experience for me.”

Solomon Wasserman, an inventor, entrepreneur and self-styled raconteur from Long Island who stopped at the rest area for coffee, said he had just driven across the bridge but was too preoccupied to notice it.

“The new bridge is open?” he said. “Mazel Tov!”

Suddenly inspired, Mr. Wasserman, 68, offered a song. With apologies to “Fiddler on the Roof,” it went like this:

If I was a rich man, ta la la la laa,

Yom pom pom pom pom pom pom,

All day long I’ll sing and I’ll celebrate

What a wonderful bridge we have! Hey!

Mr. Wasserman thanked his audience, fetched his coffee cup and got back on the road.

Correction:

An earlier version of this article misstated how long the old Tappan Zee Bridge will remain open. It will close in the fall, not when the new bridge is finished.